In the cat thought experiment, the "box" needs to be conceived of as something that totally isolates you from the cat. No "quantum influences" travel across it. Otherwise it has no point.
This is obviously impossible... hence, "thought experiment".
If you want to make the argument this makes it ultimately harder to understand rather than easier, well, I'd say the evidence overall would favor that. It seems to confuse more than it casts light on anything.
But if we did have such a box, then the cat could be alive and dead simultaneously. The dead portion of the cat superposition would consistently see the cat as dead, the living portion would consistently see the cat as alive. From within the box nothing could collapse the superposition any further. Once opened you would see only one of them. People are bothered by the macroscopic implications of this violation of our intuition of how the universe works. It is not entirely clear to me that such a violation could ever manifest in reality, though; that is one heck of a box, in a universe with gravity, neutrinos, dark matter, etc.